Skip to content

Clifford models¤

We provide exemplary 2D and 3D Clifford models as used in the paper.

All these modules are available for different algebras.

2D models¤

The following code snippet initializes a 2D Clifford ResNet.

import torch.nn.functional as F

from cliffordlayers.models.models_2d import (
    CliffordNet2d,
    CliffordBasicBlock2d,
)

model = CliffordNet2d(
        g = [-1, -1],
        block = CliffordBasicBlock2d,
        num_blocks = [2, 2, 2, 2],
        in_channels = in_channels,
        out_channels = out_channels,
        hidden_channels = 32,
        activation = F.gelu,
        norm = True,
        rotation = False,
    )

The following code snippet initializes a 2D rotational Clifford ResNet.

import torch.nn.functional as F

from cliffordlayers.models.models_2d import (
    CliffordNet2d,
    CliffordBasicBlock2d,
)

model = CliffordNet2d(
        g = [-1, -1],
        block = CliffordBasicBlock2d,
        num_blocks = [2, 2, 2, 2],
        in_channels = in_channels,
        out_channels = out_channels,
        hidden_channels = 32,
        activation = F.gelu,
        norm = True,
        rotation = True,
    )

The following code snippet initializes a 2D Clifford FNO.

import torch.nn.functional as F

from cliffordlayers.models.utils import partialclass
from cliffordlayers.models.models_2d import (
    CliffordNet2d,
    CliffordFourierBasicBlock2d,
)

model = CliffordNet2d(
        g = [-1, -1],
        block = partialclass(
                "CliffordFourierBasicBlock2d", CliffordFourierBasicBlock2d, modes1=32, modes2=32
            ),
        num_blocks = [1, 1, 1, 1],
        in_channels = in_channels,
        out_channels = out_channels,
        hidden_channels = 32,
        activation = F.gelu,
        norm = False,
        rotation = False,
    )

CliffordBasicBlock2d ¤

Bases: nn.Module

2D building block for Clifford ResNet architectures.

Parameters:

Name Type Description Default
g Union[tuple, list, torch.Tensor]

Signature of Clifford algebra.

 required
in_channels int

Number of input channels.

 required
out_channels int

Number of output channels.

 required
activation Callable

Activation function. Defaults to F.gelu.

 F.gelu
kernel_size int

Kernel size of Clifford convolution. Defaults to 3.

 3
stride int

Stride of Clifford convolution. Defaults to 1.

 1
padding int

Padding of Clifford convolution. Defaults to 1.

 1
rotation bool

Wether to use rotational Clifford convolution. Defaults to False.

 False
norm bool

Wether to use Clifford (group) normalization. Defaults to False.

 False
num_groups int

Number of groups when using Clifford (group) normalization. Defaults to 1.

 1
Source code in cliffordlayers/models/models_2d.py 
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
class CliffordBasicBlock2d(nn.Module):
    """2D building block for Clifford ResNet architectures.

    Args:
        g (Union[tuple, list, torch.Tensor]): Signature of Clifford algebra.
        in_channels (int): Number of input channels.
        out_channels (int): Number of output channels.
        activation (Callable, optional): Activation function. Defaults to F.gelu.
        kernel_size (int, optional): Kernel size of Clifford convolution. Defaults to 3.
        stride (int, optional): Stride of Clifford convolution. Defaults to 1.
        padding (int, optional): Padding of Clifford convolution. Defaults to 1.
        rotation (bool, optional): Wether to use rotational Clifford convolution. Defaults to False.
        norm (bool, optional): Wether to use Clifford (group) normalization. Defaults to False.
        num_groups (int, optional): Number of groups when using Clifford (group) normalization. Defaults to 1.
    """    
    expansion: int = 1

    def __init__(
        self,
        g: Union[tuple, list, torch.Tensor],
        in_channels: int,
        out_channels: int,
        activation: Callable = F.gelu,
        kernel_size: int = 3,
        stride: int = 1,
        padding: int = 1,
        rotation: bool = False,
        norm: bool = False,
        num_groups: int = 1,
    ) -> None:   
        super().__init__()
        self.conv1 = CliffordConv2d(
            g,
            in_channels,
            out_channels,
            kernel_size=kernel_size,
            stride=stride,
            padding=padding,
            bias=True,
            rotation=rotation,
        )
        self.conv2 = CliffordConv2d(
            g,
            out_channels,
            out_channels,
            kernel_size=kernel_size,
            stride=stride,
            padding=padding,
            bias=True,
            rotation=rotation,
        )
        self.norm1 = CliffordGroupNorm2d(g, num_groups, in_channels) if norm else nn.Identity()
        self.norm2 = CliffordGroupNorm2d(g, num_groups, out_channels) if norm else nn.Identity()
        self.activation = activation

    def __repr__(self):
        return "CliffordBasicBlock2d"

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        out = self.conv1(self.activation(self.norm1(x)))
        out = self.conv2(self.activation(self.norm2(out)))
        return out + x

CliffordFourierBasicBlock2d ¤

Bases: nn.Module

2D building block for Clifford FNO architectures.

Parameters:

Name Type Description Default
g Union[tuple, list, torch.Tensor]

Signature of Clifford algebra.

 required
in_channels int

Number of input channels.

 required
out_channels int

Number of output channels.

 required
activation Callable

Activation function. Defaults to F.gelu.

 F.gelu
kernel_size int

Kernel size of Clifford convolution. Defaults to 3.

 1
stride int

Stride of Clifford convolution. Defaults to 1.

 1
padding int

Padding of Clifford convolution. Defaults to 1.

 0
rotation bool

Wether to use rotational Clifford convolution. Defaults to False.

 False
norm bool

Wether to use Clifford (group) normalization. Defaults to False.

 False
num_groups int

Number of groups when using Clifford (group) normalization. Defaults to 1.

 1
modes1 int

Number of Fourier modes in the first dimension. Defaults to 16.

 16
modes2 int

Number of Fourier modes in the second dimension. Defaults to 16.

 16
Source code in cliffordlayers/models/models_2d.py 
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
class CliffordFourierBasicBlock2d(nn.Module):
    """2D building block for Clifford FNO architectures.

    Args:
        g (Union[tuple, list, torch.Tensor]): Signature of Clifford algebra.
        in_channels (int): Number of input channels.
        out_channels (int): Number of output channels.
        activation (Callable, optional): Activation function. Defaults to F.gelu.
        kernel_size (int, optional): Kernel size of Clifford convolution. Defaults to 3.
        stride (int, optional): Stride of Clifford convolution. Defaults to 1.
        padding (int, optional): Padding of Clifford convolution. Defaults to 1.
        rotation (bool, optional): Wether to use rotational Clifford convolution. Defaults to False.
        norm (bool, optional): Wether to use Clifford (group) normalization. Defaults to False.
        num_groups (int, optional): Number of groups when using Clifford (group) normalization. Defaults to 1.
        modes1 (int, optional): Number of Fourier modes in the first dimension. Defaults to 16.
        modes2 (int, optional): Number of Fourier modes in the second dimension. Defaults to 16.
    """   
    expansion: int = 1

    def __init__(
        self,
        g: Union[tuple, list, torch.Tensor],
        in_channels: int,
        out_channels: int,
        activation: Callable = F.gelu,
        kernel_size: int = 1,
        stride: int = 1,
        padding: int = 0,
        rotation: bool = False,
        norm: bool = False,
        num_groups: int = 1,
        modes1: int = 16,
        modes2: int = 16,
    ):   
        super().__init__()
        self.fourier = CliffordSpectralConv2d(
            g,
            in_channels,
            out_channels,
            modes1=modes1,
            modes2=modes2,
        )
        self.conv = CliffordConv2d(
            g,
            in_channels,
            out_channels,
            kernel_size=kernel_size,
            stride=stride,
            padding=padding,
            bias=True,
            rotation=rotation,
        )
        self.norm = CliffordGroupNorm2d(g, num_groups, out_channels) if norm else nn.Identity()
        self.activation = activation

    def __repr__(self):
        return "CliffordFourierBasicBlock2d"

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x1 = self.fourier(x)
        x2 = self.conv(x)
        return self.activation(self.norm(x1 + x2))

CliffordNet2d ¤

Bases: nn.Module

2D building block for Clifford architectures with ResNet backbone network.

The backbone networks follows these three steps
  1. Clifford encoding.
  2. Basic blocks as provided.
  3. Decoding.

Parameters:

Name Type Description Default
g Union[tuple, list, torch.Tensor]

Signature of Clifford algebra.

 required
block nn.Module

Choice of basic blocks.

 required
num_blocks list

List of basic blocks in each residual block.

 required
in_channels int

Number of input channels.

 required
out_channels int

Number of output channels.

 required
activation Callable

Activation function. Defaults to F.gelu.

 required
rotation bool

Wether to use rotational Clifford convolution. Defaults to False.

 required
norm bool

Wether to use Clifford (group) normalization. Defaults to False.

 False
num_groups int

Number of groups when using Clifford (group) normalization. Defaults to 1.

 1
Source code in cliffordlayers/models/models_2d.py 
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
class CliffordNet2d(nn.Module):
    """2D building block for Clifford architectures with ResNet backbone network.
    The backbone networks follows these three steps:
        1. Clifford encoding.
        2. Basic blocks as provided.
        3. Decoding.

    Args:
        g (Union[tuple, list, torch.Tensor]): Signature of Clifford algebra.
        block (nn.Module): Choice of basic blocks.
        num_blocks (list): List of basic blocks in each residual block.
        in_channels (int): Number of input channels.
        out_channels (int): Number of output channels.
        activation (Callable, optional): Activation function. Defaults to F.gelu.
        rotation (bool, optional): Wether to use rotational Clifford convolution. Defaults to False.
        norm (bool, optional): Wether to use Clifford (group) normalization. Defaults to False.
        num_groups (int, optional): Number of groups when using Clifford (group) normalization. Defaults to 1.
    """   
    # For periodic boundary conditions, set padding = 0.
    padding = 9

    def __init__(
        self,
        g: Union[tuple, list, torch.Tensor],
        block: nn.Module,
        num_blocks: list,
        in_channels: int,
        out_channels: int,
        hidden_channels: int,
        activation: Callable,
        rotation: False,
        norm: bool = False,
        num_groups: int = 1,
    ):   
        super().__init__()

        self.activation = activation
        # Encoding and decoding layers
        self.encoder = CliffordConv2dEncoder(
            g,
            in_channels=in_channels,
            out_channels=hidden_channels,
            kernel_size=1,
            padding=0,
            rotation=rotation,
        )
        self.decoder = CliffordConv2dDecoder(
            g,
            in_channels=hidden_channels,
            out_channels=out_channels,
            kernel_size=1,
            padding=0,
            rotation=rotation,
        )

        # Residual blocks
        self.layers = nn.ModuleList(
            [
                self._make_basic_block(
                    g,
                    block,
                    hidden_channels,
                    num_blocks[i],
                    activation=activation,
                    rotation=rotation,
                    norm=norm,
                    num_groups=num_groups,
                )
                for i in range(len(num_blocks))
            ]
        )

    def _make_basic_block(
        self,
        g,
        block: nn.Module,
        hidden_channels: int,
        num_blocks: int,
        activation: Callable,
        rotation: bool,
        norm: bool,
        num_groups: int,
    ) -> nn.Sequential:
        blocks = []
        for _ in range(num_blocks):
            blocks.append(
                block(
                    g,
                    hidden_channels,
                    hidden_channels,
                    activation=activation,
                    rotation=rotation,
                    norm=norm,
                    num_groups=num_groups,
                )
            )
        return nn.Sequential(*blocks)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        assert x.dim() == 5

        # Encoding layer
        x = self.encoder(self.activation(x))

        # Embed for non-periodic boundaries
        if self.padding > 0:
            B_dim, C_dim, *D_dims, I_dim = range(len(x.shape))
            x = x.permute(B_dim, I_dim, C_dim, *D_dims)
            x = F.pad(x, [0, self.padding, 0, self.padding])
            B_dim, I_dim, C_dim, *D_dims = range(len(x.shape))
            x = x.permute(B_dim, C_dim, *D_dims, I_dim)

        # Apply residual layers
        for layer in self.layers:
            x = layer(x)

        # Decoding layer
        if self.padding > 0:
            B_dim, C_dim, *D_dims, I_dim = range(len(x.shape))
            x = x.permute(B_dim, I_dim, C_dim, *D_dims)
            x = x[..., : -self.padding, : -self.padding]
            B_dim, I_dim, C_dim, *D_dims = range(len(x.shape))
            x = x.permute(B_dim, C_dim, *D_dims, I_dim)

        # Output layer
        x = self.decoder(x)
        return x

3D models¤

The following code snippet initializes a 3D Clifford FNO.

import torch.nn.functional as F

from cliffordlayers.models.models_3d import (
    CliffordNet3d,
    CliffordFourierBasicBlock3d,
)
model = CliffordNet3d(
        g = [1, 1, 1],
        block = CliffordFourierBasicBlock3d,
        num_blocks = [1, 1, 1, 1],
        in_channels = 4,
        out_channels = 1,
        hidden_channels = 16,
        activation = F.gelu,
        norm = False,
    )

CliffordFourierBasicBlock3d ¤

Bases: nn.Module

2D building block for Clifford FNO architectures.

Parameters:

Name Type Description Default
g Union[tuple, list, torch.Tensor]

Signature of Clifford algebra.

 required
in_channels int

Number of input channels.

 required
out_channels int

Number of output channels.

 required
activation Callable

Activation function. Defaults to F.gelu.

 F.gelu
kernel_size int

Kernel size of Clifford convolution. Defaults to 3.

 1
stride int

Stride of Clifford convolution. Defaults to 1.

 1
padding int

Padding of Clifford convolution. Defaults to 1.

 0
norm bool

Wether to use Clifford (group) normalization. Defaults to False.

 False
num_groups int

Number of groups when using Clifford (group) normalization. Defaults to 1.

 1
modes1 int

Number of Fourier modes in the first dimension. Defaults to 8.

 8
modes2 int

Number of Fourier modes in the second dimension. Defaults to 8.

 8
modes3 int

Number of Fourier modes in the third dimension. Defaults to 8.

 8
Source code in cliffordlayers/models/models_3d.py 
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
class CliffordFourierBasicBlock3d(nn.Module):
    """2D building block for Clifford FNO architectures.

        Args:
            g (Union[tuple, list, torch.Tensor]): Signature of Clifford algebra.
            in_channels (int): Number of input channels.
            out_channels (int): Number of output channels.
            activation (Callable, optional): Activation function. Defaults to F.gelu.
            kernel_size (int, optional): Kernel size of Clifford convolution. Defaults to 3.
            stride (int, optional): Stride of Clifford convolution. Defaults to 1.
            padding (int, optional): Padding of Clifford convolution. Defaults to 1.
            norm (bool, optional): Wether to use Clifford (group) normalization. Defaults to False.
            num_groups (int, optional): Number of groups when using Clifford (group) normalization. Defaults to 1.
            modes1 (int, optional): Number of Fourier modes in the first dimension. Defaults to 8.
            modes2 (int, optional): Number of Fourier modes in the second dimension. Defaults to 8.
            modes3 (int, optional): Number of Fourier modes in the third dimension. Defaults to 8.
        """    
    expansion: int = 1

    def __init__(
        self,
        g: Union[tuple, list, torch.Tensor],
        in_channels: int,
        out_channels: int,
        activation: Callable = F.gelu,
        kernel_size: int = 1,
        stride: int = 1,
        padding: int = 0,
        norm: bool = False,
        num_groups: int = 1,
        modes1: int = 8,
        modes2: int = 8,
        modes3: int = 8,
    ):    
        super().__init__()
        self.fourier = CliffordSpectralConv3d(
            g,
            in_channels,
            out_channels,
            modes1=modes1,
            modes2=modes2,
            modes3=modes3,
        )
        self.conv = CliffordConv3d(
            g,
            in_channels,
            out_channels,
            kernel_size=kernel_size,
            stride=stride,
            padding=padding,
            bias=True,
        )
        self.norm = CliffordGroupNorm3d(g, num_groups, in_channels) if norm else nn.Identity()
        self.activation = activation

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x1 = self.fourier(x)
        x2 = self.conv(x)
        return self.activation(self.norm(x1 + x2))

CliffordNet3d ¤

Bases: nn.Module

3D building block for Clifford architectures with ResNet backbone network.

The backbone networks follows these three steps
  1. Clifford encoding.
  2. Basic blocks as provided.
  3. Decoding.

Parameters:

Name Type Description Default
g Union[tuple, list, torch.Tensor]

Signature of Clifford algebra.

 required
block nn.Module

Choice of basic blocks.

 required
num_blocks list

List of basic blocks in each residual block.

 required
in_channels int

Number of input channels.

 required
out_channels int

Number of output channels.

 required
activation Callable

Activation function. Defaults to F.gelu.

 required
norm bool

Wether to use Clifford (group) normalization. Defaults to False.

 False
num_groups int

Number of groups when using Clifford (group) normalization. Defaults to 1.

 1
Source code in cliffordlayers/models/models_3d.py 
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
class CliffordNet3d(nn.Module):
    """3D building block for Clifford architectures with ResNet backbone network.
    The backbone networks follows these three steps:
        1. Clifford encoding.
        2. Basic blocks as provided.
        3. Decoding.

    Args:
        g (Union[tuple, list, torch.Tensor]): Signature of Clifford algebra.
        block (nn.Module): Choice of basic blocks.
        num_blocks (list): List of basic blocks in each residual block.
        in_channels (int): Number of input channels.
        out_channels (int): Number of output channels.
        activation (Callable, optional): Activation function. Defaults to F.gelu.
        norm (bool, optional): Wether to use Clifford (group) normalization. Defaults to False.
        num_groups (int, optional): Number of groups when using Clifford (group) normalization. Defaults to 1.
    """     
    # For periodic boundary conditions, set padding = 0.
    padding = 2

    def __init__(
        self,
        g: Union[tuple, list, torch.Tensor],
        block: nn.Module,
        num_blocks: list,
        in_channels: int,
        out_channels: int,
        hidden_channels: int,
        activation: Callable,
        norm: bool = False,
        num_groups: int = 1,
    ):
        super().__init__()

        self.activation = activation
        # Encoding and decoding layers.
        self.encoder = CliffordConv3dEncoder(
            g,
            in_channels=in_channels,
            out_channels=hidden_channels,
            kernel_size=1,
            padding=0,
        )
        self.decoder = CliffordConv3dDecoder(
            g,
            in_channels=hidden_channels,
            out_channels=out_channels,
            kernel_size=1,
            padding=0,
        )

        # Residual blocks.
        self.layers = nn.ModuleList(
            [
                self._make_basic_block(
                    g,
                    block,
                    hidden_channels,
                    num_blocks[i],
                    activation=activation,
                    norm=norm,
                    num_groups=num_groups,
                )
                for i in range(len(num_blocks))
            ]
        )

    def _make_basic_block(
        self,
        g,
        block: nn.Module,
        hidden_channels: int,
        num_blocks: int,
        activation: Callable,
        norm: bool,
        num_groups: int,
    ) -> nn.Sequential:
        blocks = []
        for _ in range(num_blocks):
            blocks.append(
                block(
                    g,
                    hidden_channels,
                    hidden_channels,
                    activation=activation,
                    norm=norm,
                    num_groups=num_groups,
                )
            )
        return nn.Sequential(*blocks)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        assert x.dim() == 6

        # Encoding layer.
        x = self.encoder(self.activation(x))

        # Embed for non-periodic boundaries.
        if self.padding > 0:
            B_dim, C_dim, *D_dims, I_dim = range(len(x.shape))
            x = x.permute(B_dim, I_dim, C_dim, *D_dims)
            x = F.pad(x, [0, self.padding, 0, self.padding, 0, self.padding])
            B_dim, I_dim, C_dim, *D_dims = range(len(x.shape))
            x = x.permute(B_dim, C_dim, *D_dims, I_dim)

        # Apply residual layers.
        for layer in self.layers:
            x = layer(x)

        # Decoding layer.
        if self.padding > 0:
            B_dim, C_dim, *D_dims, I_dim = range(len(x.shape))
            x = x.permute(B_dim, I_dim, C_dim, *D_dims)
            x = x[..., : -self.padding, : -self.padding, : -self.padding]
            B_dim, I_dim, C_dim, *D_dims = range(len(x.shape))
            x = x.permute(B_dim, C_dim, *D_dims, I_dim)

        # Output layer.
        x = self.decoder(x)
        return x